Using RAW here gives you a much larger range of adjustment before getting image degradation. The reason is that the JPEG is only 256 levels of brightness, while the RAW file may have up to 16,000 levels of brightness (for a 14 bit file, if you have a 12 bit file it is "only" 4096 levels). These extra levels give you a lot more dynamic range to pull details out of the shadows.

The reason I suggested the 85 f/1.8 and the 135 f/2 is that they have an f-stop advantage over even the 70-200 f/2.8, and that is a factor of two in shutter speed, which can be crucial. Having said that, I have shot some BB pictures at stop points using the 70-200 f/4 at 1/200 at ISO 3200 on a monopod ( I needed 170mm to get enough reach, and the lighting was better than normal). The main disadvantage of the 70 - 200 f/2.8 ( with all due respect to those devoted to that lens ) is both its weight and its size. 75 per cent of my competition gymnastics pictures are shot with the 85; the 135L is nice to have when you either want a more intimate framing or you need the reach. A 40D with the 85 f/1.8 mounted is relatively light weight and unobtrusive. All four of these lenses ( 85 f/1.8, 135 f/2, 70 - 200 f/2.8 and 70 - 200 f/4) have very fast, accurate AF in my experience.

As I pointed out in my original post, and others have reiterated, you need to shoot in RAW mode, not JPEG. This to preserve the maximum dynamic range for post-processing using DPP or whatever other RAW converter of your choice. Some of this is for exposure adjustment, although usually not that much ( I usually end up pushing it down 1/3 stop or so) but mainly for white balance adjustment. All gyms are different in the type and quality of the lighting ( some have skylights which mixes sunlight in with the rest of it ) and I find myself adjusting the WB on a shot to shot basis in many gyms ( usually you can find some nominally white or gray object either in the scene or on the gymnast to use as a test card). You also need to pay some attention to the metering on the different events; I know of at least one gym where the exposure changes by 1 1/2 f-stops from one side of the gym to the other.

Take lots of pictures; there will be some keepers in there. Pro photographers shoot hundreds to thousands to get the really good ones.